{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimization Methods\n",
    "\n",
    "直到现在，你已经使用了梯度下降算法来更新参数并最小化cost。在本次实验中，你将会学到使用更多的高级的方法来加速学习或者得到更好的训练结果。一个好的优化算法能够让你将训练时间从几天缩短到几个小时！\n",
    "\n",
    "梯度下降算法可以描述为一个人从山顶往山脚下走，如下图所示: \n",
    "\n",
    "<img src=\"images/cost.jpg\" style=\"width:650px;height:300px;\">\n",
    "<caption><center> <u> **图 1** </u>: **最小化cost的工作类似于找到山地中的最低点**<br> 训练过程中的每次迭代相当于往山地最低点的方向迈了一步. </center></caption>\n",
    "\n",
    "**注意**: 还是一样, 使用 `da` 表示 $\\frac{\\partial J}{\\partial a }  $.\n",
    "\n",
    "引入一些需要用到的库文件："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/starwe/Desktop/百度工作/DeepLearningAndPaddleTutorial/jupyter/10.optimization/numpy_optimization/Optimization/opt_utils.py:76: SyntaxWarning: assertion is always true, perhaps remove parentheses?\n",
      "  assert(parameters['W' + str(l)].shape == layer_dims[l], layer_dims[l-1])\n",
      "/Users/starwe/Desktop/百度工作/DeepLearningAndPaddleTutorial/jupyter/10.optimization/numpy_optimization/Optimization/opt_utils.py:77: SyntaxWarning: assertion is always true, perhaps remove parentheses?\n",
      "  assert(parameters['W' + str(l)].shape == layer_dims[l], 1)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io\n",
    "import math\n",
    "import sklearn\n",
    "import sklearn.datasets\n",
    "\n",
    "from opt_utils import load_params_and_grads, initialize_parameters, forward_propagation, backward_propagation\n",
    "from opt_utils import compute_cost, predict, predict_dec, plot_decision_boundary, load_dataset\n",
    "from testCases import *\n",
    "\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (7.0, 4.0) # set default size of plots\n",
    "plt.rcParams['image.interpolation'] = 'nearest'\n",
    "plt.rcParams['image.cmap'] = 'gray'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1 - Gradient Descent\n",
    "\n",
    "一个简单的机器学习优化方法就是梯度下降gradient descent (GD). 当你在每一步都对所有的$m$ 个样例使用梯度下降，那么这样的梯度下降方法叫做Batch Gradient Descent. \n",
    "\n",
    "**热身练习**: 实现梯度下降更新规则，对于 $l = 1, ..., L$: \n",
    "$$ W^{[l]} = W^{[l]} - \\alpha \\text{ } dW^{[l]} \\tag{1}$$\n",
    "$$ b^{[l]} = b^{[l]} - \\alpha \\text{ } db^{[l]} \\tag{2}$$\n",
    "\n",
    "L 表示第几层、 $\\alpha$ 表示学习率. 所有参数都储存在 `parameters` 字典中国年. 注意到第一次迭代 `l` 在 `for` 循环中应该为0， 而第一个参数是 $W^{[1]}$ and $b^{[1]}$。所以我们需要将`l` 表示为 `l+1` 。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters_with_gd\n",
    "\n",
    "def update_parameters_with_gd(parameters, grads, learning_rate):\n",
    "    \"\"\"\n",
    "    Update parameters using one step of gradient descent\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters to be updated:\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    grads -- python dictionary containing your gradients to update each parameters:\n",
    "                    grads['dW' + str(l)] = dWl\n",
    "                    grads['db' + str(l)] = dbl\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    \n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    \"\"\"\n",
    "\n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "\n",
    "    # Update rule for each parameter\n",
    "    for l in range(L):\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        parameters[\"W\" + str(l+1)] = parameters[\"W\" + str(l+1)] - learning_rate * grads[\"dW\" + str(l+1)]\n",
    "        parameters[\"b\" + str(l+1)] = parameters[\"b\" + str(l+1)] - learning_rate * grads[\"db\" + str(l+1)]\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[ 1.63535156 -0.62320365 -0.53718766]\n",
      " [-1.07799357  0.85639907 -2.29470142]]\n",
      "b1 = [[ 1.74604067]\n",
      " [-0.75184921]]\n",
      "W2 = [[ 0.32171798 -0.25467393  1.46902454]\n",
      " [-2.05617317 -0.31554548 -0.3756023 ]\n",
      " [ 1.1404819  -1.09976462 -0.1612551 ]]\n",
      "b2 = [[-0.88020257]\n",
      " [ 0.02561572]\n",
      " [ 0.57539477]]\n"
     ]
    }
   ],
   "source": [
    "parameters, grads, learning_rate = update_parameters_with_gd_test_case()\n",
    "\n",
    "parameters = update_parameters_with_gd(parameters, grads, learning_rate)\n",
    "print(\"W1 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**期望输出**:\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "    <td > **W1** </td> \n",
    "           <td > [[ 1.63535156 -0.62320365 -0.53718766]\n",
    " [-1.07799357  0.85639907 -2.29470142]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b1** </td> \n",
    "           <td > [[ 1.74604067]\n",
    " [-0.75184921]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **W2** </td> \n",
    "           <td > [[ 0.32171798 -0.25467393  1.46902454]\n",
    " [-2.05617317 -0.31554548 -0.3756023 ]\n",
    " [ 1.1404819  -1.09976462 -0.1612551 ]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b2** </td> \n",
    "           <td > [[-0.88020257]\n",
    " [ 0.02561572]\n",
    " [ 0.57539477]] </td> \n",
    "    </tr> \n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "随机梯度下降Stochastic Gradient Descent(SGD)与 (batch) gradient descent相似，不同之处在于随机梯度下降每次只根据单个样例进行梯度下降并更新参数，而不是使用整个训练集。下面的代码表示了两者的不同：\n",
    "\n",
    "- **(Batch) Gradient Descent**:\n",
    "\n",
    "``` python\n",
    "X = data_input\n",
    "Y = labels\n",
    "parameters = initialize_parameters(layers_dims)\n",
    "for i in range(0, num_iterations):\n",
    "    # Forward propagation\n",
    "    a, caches = forward_propagation(X, parameters)\n",
    "    # Compute cost.\n",
    "    cost = compute_cost(a, Y)\n",
    "    # Backward propagation.\n",
    "    grads = backward_propagation(a, caches, parameters)\n",
    "    # Update parameters.\n",
    "    parameters = update_parameters(parameters, grads)\n",
    "        \n",
    "```\n",
    "\n",
    "- **Stochastic Gradient Descent**:\n",
    "\n",
    "```python\n",
    "X = data_input\n",
    "Y = labels\n",
    "parameters = initialize_parameters(layers_dims)\n",
    "for i in range(0, num_iterations):\n",
    "    for j in range(0, m):\n",
    "        # Forward propagation\n",
    "        a, caches = forward_propagation(X[:,j], parameters)\n",
    "        # Compute cost\n",
    "        cost = compute_cost(a, Y[:,j])\n",
    "        # Backward propagation\n",
    "        grads = backward_propagation(a, caches, parameters)\n",
    "        # Update parameters.\n",
    "        parameters = update_parameters(parameters, grads)\n",
    "```\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在随机梯度下降(Stochastic Gradient Descent)中, 我们使用单个样例来计算梯度。当训练集很大时, SGD 会很快。但是参数的收敛过程会出现震荡。如图所示: \n",
    "\n",
    "<img src=\"images/kiank_sgd.png\" style=\"width:750px;height:250px;\">\n",
    "<caption><center> <u> <font color='purple'> **图 1** </u><font color='purple'>  : **SGD vs GD**<br> \"+\" 表示cost最小值点。 SGD 的收敛过程产生很大的震荡. 但是 SGD 的每一次迭代比 GD 要快得多, 因为它只使用了单个样例来计算 (vs. GD使用了整个训练集). </center></caption>\n",
    "\n",
    "**注意** 实现 SGD 总共需要3个for循环:\n",
    "1. 迭代次数(number of iterations)\n",
    "2. 训练集样例数 $m$ (training examples)\n",
    "3. 神经网络层数 (更新参数，从$(W^{[1]},b^{[1]})$ 到 $(W^{[L]},b^{[L]})$)\n",
    "\n",
    "在实践中，如果你不使用整个训练集，也不仅仅是一个训练样例来执行每个更新，通常会得到更快的结果。小批量梯度下降(Mini-Batch GD)使用的样例数介于一个和整个训练集样例数之间。通过小批量梯度下降，可以循环使用小批量，而不是循环遍历各个训练样例。\n",
    "\n",
    "<img src=\"images/kiank_minibatch.png\" style=\"width:750px;height:250px;\">\n",
    "<caption><center> <u> <font color='purple'> **图 2** </u>: <font color='purple'>  **SGD vs Mini-Batch GD**<br> \"+\" 代表cost最小值点. 使用mini-batches往往能导致更快的收敛速度. </center></caption>\n",
    "\n",
    "<font color='blue'>\n",
    "**你应该记住：**:\n",
    "- gradient descent, mini-batch gradient descent and stochastic gradient descent之间的不同在于每次迭代更新使用的样例数量不同。\n",
    "- 你需要调整学习率 $\\alpha$.\n",
    "- 一个调整好的 mini-batch size, 通常表现的比 gradient descent 或者 stochastic gradient descent 都好(尤其是当训练集很大的时候)。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 - Mini-Batch Gradient descent\n",
    "\n",
    "让我们学习怎么从训练集(X, Y)中构建Mini-Batch。\n",
    "\n",
    "两个步骤:\n",
    "- **Shuffle**: 构建一个“乱序”的数据集 (X, Y)。没列的X 和 Y代表一个训练样例。需要注意的是“乱序”的操作对于 X 和 Y是同步的。只有这样，“乱序”后的数据集中， X 的 $i^{th}$ 个值才会对应着 Y 的 $i^{th}$ 的标签值. “乱序”操作保证所有的样例都被分配到不同的Mini-Batch中。\n",
    "\n",
    "<img src=\"images/kiank_shuffle.png\" style=\"width:550px;height:300px;\">\n",
    "\n",
    "- **分割数据**: 分割 shuffled (X, Y) 为 `mini_batch_size`（这里是64）大小的mini-batches 。需要注意的是训练样例的数量并不总是能被 `mini_batch_size` 整除。最后一个Mini-Batch会比其它Mini-Batch小,  它看起来是这样的: \n",
    "\n",
    "<img src=\"images/kiank_partition.png\" style=\"width:550px;height:300px;\">\n",
    "\n",
    "**练习**: 实现 `random_mini_batches`。我们已经帮你实现了“乱序”的方法. 你可以通过下面的方法来分割 $1^{st}$ and $2^{nd}$ mini-batches:\n",
    "```python\n",
    "first_mini_batch_X = shuffled_X[:, 0 : mini_batch_size]\n",
    "second_mini_batch_X = shuffled_X[:, mini_batch_size : 2 * mini_batch_size]\n",
    "...\n",
    "```\n",
    "\n",
    "最后一个Mini-Batch可能小于 `mini_batch_size=64`. 用 $\\lfloor s \\rfloor$ 表示 $s$ 向下取整 ( `math.floor(s)` in Python). 如果样例总数不能被 `mini_batch_size=64` 整除，那么会有 $\\lfloor \\frac{m}{mini\\_batch\\_size}\\rfloor$ mini-batches包含64个样例, 而最后一个mini-batch的样例数会是($m-mini_\\_batch_\\_size \\times \\lfloor \\frac{m}{mini\\_batch\\_size}\\rfloor$). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: random_mini_batches\n",
    "\n",
    "def random_mini_batches(X, Y, mini_batch_size = 64, seed = 0):\n",
    "    \"\"\"\n",
    "    Creates a list of random minibatches from (X, Y)\n",
    "    \n",
    "    Arguments:\n",
    "    X -- input data, of shape (input size, number of examples)\n",
    "    Y -- true \"label\" vector (1 for blue dot / 0 for red dot), of shape (1, number of examples)\n",
    "    mini_batch_size -- size of the mini-batches, integer\n",
    "    \n",
    "    Returns:\n",
    "    mini_batches -- list of synchronous (mini_batch_X, mini_batch_Y)\n",
    "    \"\"\"\n",
    "    \n",
    "    np.random.seed(seed)            # To make your \"random\" minibatches the same as ours\n",
    "    m = X.shape[1]                  # number of training examples\n",
    "    mini_batches = []\n",
    "        \n",
    "    # Step 1: Shuffle (X, Y)\n",
    "    permutation = list(np.random.permutation(m))\n",
    "    shuffled_X = X[:, permutation]\n",
    "    shuffled_Y = Y[:, permutation].reshape((1,m))\n",
    "\n",
    "    # Step 2: Partition (shuffled_X, shuffled_Y). Minus the end case.\n",
    "    num_complete_minibatches = math.floor(m/mini_batch_size) # number of mini batches of size mini_batch_size in your partitionning\n",
    "    for k in range(0, num_complete_minibatches):\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        mini_batch_X = shuffled_X[:, k * mini_batch_size : (k + 1) * mini_batch_size]\n",
    "        mini_batch_Y = shuffled_Y[:, k * mini_batch_size : (k + 1) * mini_batch_size]\n",
    "        ### END CODE HERE ###\n",
    "        mini_batch = (mini_batch_X, mini_batch_Y)\n",
    "        mini_batches.append(mini_batch)\n",
    "    \n",
    "    # Handling the end case (last mini-batch < mini_batch_size)\n",
    "    if m % mini_batch_size != 0:\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        mini_batch_X = shuffled_X[:, num_complete_minibatches * mini_batch_size : m]\n",
    "        mini_batch_Y = shuffled_Y[:, num_complete_minibatches * mini_batch_size : m]\n",
    "        ### END CODE HERE ###\n",
    "        mini_batch = (mini_batch_X, mini_batch_Y)\n",
    "        mini_batches.append(mini_batch)\n",
    "    \n",
    "    return mini_batches"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shape of the 1st mini_batch_X: (12288, 64)\n",
      "shape of the 2nd mini_batch_X: (12288, 64)\n",
      "shape of the 3rd mini_batch_X: (12288, 20)\n",
      "shape of the 1st mini_batch_Y: (1, 64)\n",
      "shape of the 2nd mini_batch_Y: (1, 64)\n",
      "shape of the 3rd mini_batch_Y: (1, 20)\n",
      "mini batch sanity check: [ 0.90085595 -0.7612069   0.2344157 ]\n"
     ]
    }
   ],
   "source": [
    "X_assess, Y_assess, mini_batch_size = random_mini_batches_test_case()\n",
    "mini_batches = random_mini_batches(X_assess, Y_assess, mini_batch_size)\n",
    "\n",
    "print (\"shape of the 1st mini_batch_X: \" + str(mini_batches[0][0].shape))\n",
    "print (\"shape of the 2nd mini_batch_X: \" + str(mini_batches[1][0].shape))\n",
    "print (\"shape of the 3rd mini_batch_X: \" + str(mini_batches[2][0].shape))\n",
    "print (\"shape of the 1st mini_batch_Y: \" + str(mini_batches[0][1].shape))\n",
    "print (\"shape of the 2nd mini_batch_Y: \" + str(mini_batches[1][1].shape)) \n",
    "print (\"shape of the 3rd mini_batch_Y: \" + str(mini_batches[2][1].shape))\n",
    "print (\"mini batch sanity check: \" + str(mini_batches[0][0][0][0:3]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**期望输出**:\n",
    "\n",
    "<table style=\"width:50%\"> \n",
    "    <tr>\n",
    "    <td > **shape of the 1st mini_batch_X** </td> \n",
    "           <td > (12288, 64) </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **shape of the 2nd mini_batch_X** </td> \n",
    "           <td > (12288, 64) </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **shape of the 3rd mini_batch_X** </td> \n",
    "           <td > (12288, 20) </td> \n",
    "    </tr>\n",
    "    <tr>\n",
    "    <td > **shape of the 1st mini_batch_Y** </td> \n",
    "           <td > (1, 64) </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **shape of the 2nd mini_batch_Y** </td> \n",
    "           <td > (1, 64) </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **shape of the 3rd mini_batch_Y** </td> \n",
    "           <td > (1, 20) </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **mini batch sanity check** </td> \n",
    "           <td > [ 0.90085595 -0.7612069   0.2344157 ] </td> \n",
    "    </tr>\n",
    "    \n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "**你应该记住**:\n",
    "- 要构造mini-batches，我们需要实现“乱序”和分割数据两个步骤(Shuffling and Partitioning)\n",
    "- 我们通常选择2的n次方作为mini-batch size, e.g., 16, 32, 64, 128."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3 - Momentum\n",
    "\n",
    "Because mini-batch gradient descent makes a parameter update after seeing just a subset of examples, the direction of the update has some variance, and so the path taken by mini-batch gradient descent will \"oscillate\" toward convergence. Using momentum can reduce these oscillations. \n",
    "\n",
    "Momentum takes into account the past gradients to smooth out the update. We will store the 'direction' of the previous gradients in the variable $v$. Formally, this will be the exponentially weighted average of the gradient on previous steps. You can also think of $v$ as the \"velocity\" of a ball rolling downhill, building up speed (and momentum) according to the direction of the gradient/slope of the hill. \n",
    "\n",
    "由于小批量梯度下降在仅看到一个子集的样例之后进行参数更新，因此更新的方向有一定的变化，所以小批量梯度下降所采用的路径将会“趋于”收敛。 使用动量可以减少这些振荡。\n",
    "\n",
    "动量利用之前步骤的梯度值来平滑更新的过程。 我们将把之前步骤的梯度“方向”存储在变量$ v $中。 形式上，这将是前面步骤中梯度的指数加权平均值。 你也可以把$ v $想象成一个下坡滚动的“速度”，根据山坡的坡度/方向建立速度（和动量）。\n",
    "\n",
    "<img src=\"images/opt_momentum.png\" style=\"width:400px;height:250px;\">\n",
    "<caption><center> <u><font color='purple'>**图 3**</u><font color='purple'>: 红色的箭头表示mini-batch gradient descent with momentum的一次梯度下降方向. 蓝色的虚线表示当前的Mini-Batch计算的梯度下降方向。我们用梯度值来计算$v$然后用$v$来更新参数.<br> <font color='black'> </center>\n",
    "\n",
    "\n",
    "**练习**: 初始化速度(velocity)。速度 $v$, 初始化为一个值为零的python字典。他的keys与 `grads` 相同：\n",
    "对于 $l =1,...,L$:\n",
    "```python\n",
    "v[\"dW\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"W\" + str(l+1)])\n",
    "v[\"db\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"b\" + str(l+1)])\n",
    "```\n",
    "**注意** 到第一次迭代 `l` 在 `for` 循环中应该为0， 而第一个参数是 $W^{[1]}$ and $b^{[1]}$。所以我们需要将`l` 表示为 `l+1` 。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: initialize_velocity\n",
    "\n",
    "def initialize_velocity(parameters):\n",
    "    \"\"\"\n",
    "    Initializes the velocity as a python dictionary with:\n",
    "                - keys: \"dW1\", \"db1\", ..., \"dWL\", \"dbL\" \n",
    "                - values: numpy arrays of zeros of the same shape as the corresponding gradients/parameters.\n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters.\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    \n",
    "    Returns:\n",
    "    v -- python dictionary containing the current velocity.\n",
    "                    v['dW' + str(l)] = velocity of dWl\n",
    "                    v['db' + str(l)] = velocity of dbl\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "    v = {}\n",
    "    \n",
    "    # Initialize velocity\n",
    "    for l in range(L):\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        v[\"dW\" + str(l+1)] = np.zeros(parameters['W' + str(l+1)].shape)\n",
    "        v[\"db\" + str(l+1)] = np.zeros(parameters['b' + str(l+1)].shape)\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "    return v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v[\"dW1\"] = [[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "v[\"db1\"] = [[ 0.]\n",
      " [ 0.]]\n",
      "v[\"dW2\"] = [[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "v[\"db2\"] = [[ 0.]\n",
      " [ 0.]\n",
      " [ 0.]]\n"
     ]
    }
   ],
   "source": [
    "parameters = initialize_velocity_test_case()\n",
    "\n",
    "v = initialize_velocity(parameters)\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**期望输出**:\n",
    "\n",
    "<table style=\"width:40%\"> \n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**练习**:  现在用momentum来实现参数更新. Momentum参数更新规则是，对于 $l = 1, ..., L$: \n",
    "\n",
    "$$ \\begin{cases}\n",
    "v_{dW^{[l]}} = \\beta v_{dW^{[l]}} + (1 - \\beta) dW^{[l]} \\\\\n",
    "W^{[l]} = W^{[l]} - \\alpha v_{dW^{[l]}}\n",
    "\\end{cases}\\tag{3}$$\n",
    "\n",
    "$$\\begin{cases}\n",
    "v_{db^{[l]}} = \\beta v_{db^{[l]}} + (1 - \\beta) db^{[l]} \\\\\n",
    "b^{[l]} = b^{[l]} - \\alpha v_{db^{[l]}} \n",
    "\\end{cases}\\tag{4}$$\n",
    "\n",
    "L表示神经网络的第几层， $\\beta$ 表示momentum参数，$\\alpha$ 表示学习率。 所有参数都需要存储在 `parameters` 字典中. **注意** 到第一次迭代 `l` 在 `for` 循环中应该为0， 而第一个参数是 $W^{[1]}$ and $b^{[1]}$。所以我们需要将`l` 表示为 `l+1` 。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters_with_momentum\n",
    "\n",
    "def update_parameters_with_momentum(parameters, grads, v, beta, learning_rate):\n",
    "    \"\"\"\n",
    "    Update parameters using Momentum\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters:\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    grads -- python dictionary containing your gradients for each parameters:\n",
    "                    grads['dW' + str(l)] = dWl\n",
    "                    grads['db' + str(l)] = dbl\n",
    "    v -- python dictionary containing the current velocity:\n",
    "                    v['dW' + str(l)] = ...\n",
    "                    v['db' + str(l)] = ...\n",
    "    beta -- the momentum hyperparameter, scalar\n",
    "    learning_rate -- the learning rate, scalar\n",
    "    \n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    v -- python dictionary containing your updated velocities\n",
    "    \"\"\"\n",
    "\n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "    # print(parameters)\n",
    "    # Momentum update for each parameter\n",
    "    for l in range(L):\n",
    "        \n",
    "        ### START CODE HERE ### (approx. 4 lines)\n",
    "        # compute velocities\n",
    "        v[\"dW\" + str(l+1)] = beta * v[\"dW\" + str(l+1)] + (1 - beta) * grads[\"dW\" + str(l+1)]\n",
    "        v[\"db\" + str(l+1)] = beta * v[\"db\" + str(l+1)] + (1 - beta) * grads[\"db\" + str(l+1)]\n",
    "        # update parameters\n",
    "        parameters[\"W\" + str(l+1)] = parameters[\"W\" + str(l+1)] - learning_rate * v[\"dW\" + str(l+1)]\n",
    "        parameters[\"b\" + str(l+1)] = parameters[\"b\" + str(l+1)] - learning_rate * v[\"db\" + str(l+1)]\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "    return parameters, v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[ 1.62544598 -0.61290114 -0.52907334]\n",
      " [-1.07347112  0.86450677 -2.30085497]]\n",
      "b1 = [[ 1.74493465]\n",
      " [-0.76027113]]\n",
      "W2 = [[ 0.31930698 -0.24990073  1.4627996 ]\n",
      " [-2.05974396 -0.32173003 -0.38320915]\n",
      " [ 1.13444069 -1.0998786  -0.1713109 ]]\n",
      "b2 = [[-0.87809283]\n",
      " [ 0.04055394]\n",
      " [ 0.58207317]]\n",
      "v[\"dW1\"] = [[-0.11006192  0.11447237  0.09015907]\n",
      " [ 0.05024943  0.09008559 -0.06837279]]\n",
      "v[\"db1\"] = [[-0.01228902]\n",
      " [-0.09357694]]\n",
      "v[\"dW2\"] = [[-0.02678881  0.05303555 -0.06916608]\n",
      " [-0.03967535 -0.06871727 -0.08452056]\n",
      " [-0.06712461 -0.00126646 -0.11173103]]\n",
      "v[\"db2\"] = [[ 0.02344157]\n",
      " [ 0.16598022]\n",
      " [ 0.07420442]]\n"
     ]
    }
   ],
   "source": [
    "parameters, grads, v = update_parameters_with_momentum_test_case()\n",
    "\n",
    "parameters, v = update_parameters_with_momentum(parameters, grads, v, beta = 0.9, learning_rate = 0.01)\n",
    "print(\"W1 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:90%\"> \n",
    "    <tr>\n",
    "    <td > **W1** </td> \n",
    "           <td > [[ 1.62544598 -0.61290114 -0.52907334]\n",
    " [-1.07347112  0.86450677 -2.30085497]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b1** </td> \n",
    "           <td > [[ 1.74493465]\n",
    " [-0.76027113]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **W2** </td> \n",
    "           <td > [[ 0.31930698 -0.24990073  1.4627996 ]\n",
    " [-2.05974396 -0.32173003 -0.38320915]\n",
    " [ 1.13444069 -1.0998786  -0.1713109 ]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b2** </td> \n",
    "           <td > [[-0.87809283]\n",
    " [ 0.04055394]\n",
    " [ 0.58207317]] </td> \n",
    "    </tr> \n",
    "\n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[-0.11006192  0.11447237  0.09015907]\n",
    " [ 0.05024943  0.09008559 -0.06837279]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[-0.01228902]\n",
    " [-0.09357694]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[-0.02678881  0.05303555 -0.06916608]\n",
    " [-0.03967535 -0.06871727 -0.08452056]\n",
    " [-0.06712461 -0.00126646 -0.11173103]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.02344157]\n",
    " [ 0.16598022]\n",
    " [ 0.07420442]]</td> \n",
    "    </tr> \n",
    "</table>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**注意** :\n",
    "- velocity初始化为零。所以算法需要几次迭代才能开始加速，加快学习速度。\n",
    "- 如果 $\\beta = 0$则相当于不使用Momentum。 \n",
    "\n",
    "**如何选择 $\\beta$?**\n",
    "\n",
    "- $\\beta$ 越大，更新过程越平滑（因为我们受到更多的之前的梯度值的影响），但是如果 $\\beta$ 太大, 会使得更新过程过度平滑。\n",
    "- 一般的 $\\beta$ 值的选择介于 0.8 到 0.999。如果你不想自己尝试调整, $\\beta = 0.9$ 是不错的选择。 \n",
    "- 你可能需要多次尝试来找到最好的 $\\beta$ 值，来使你的模型训练出最小的cost function $J$。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "**你应该记住：**:\n",
    "- Momentum 让收敛过程更平滑，它可以被是用在batch gradient descent, mini-batch gradient descent 或者 stochastic gradient descent.\n",
    "- 你需要调整momentum参数 $\\beta$ 和学习率参数 $\\alpha$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4 - Adam\n",
    "\n",
    "Adam是十分有效的训练神经网络的优化算法。它结合了RMSProp 和 Momentum方法。\n",
    "\n",
    "**Adam是如何工作的?**\n",
    "\n",
    "1. 它计算过去梯度的指数加权平均，并将其存储在变量$ v $（before bias correction）和$ v ^ {corrected} $（with bias correction）中。\n",
    "2. 它计算过去梯度的平方的指数加权平均值，并将其存储在变量$ s $（before bias correction）和$ s ^ {corrected} $（with bias correction）中。\n",
    "3. 根据1 和 2 中的计算值进行参数更新。\n",
    "\n",
    "更新规则是，对于 $l = 1, ..., L$: \n",
    "\n",
    "$$\\begin{cases}\n",
    "v_{dW^{[l]}} = \\beta_1 v_{dW^{[l]}} + (1 - \\beta_1) \\frac{\\partial \\mathcal{J} }{ \\partial W^{[l]} } \\\\\n",
    "v^{corrected}_{dW^{[l]}} = \\frac{v_{dW^{[l]}}}{1 - (\\beta_1)^t} \\\\\n",
    "s_{dW^{[l]}} = \\beta_2 s_{dW^{[l]}} + (1 - \\beta_2) (\\frac{\\partial \\mathcal{J} }{\\partial W^{[l]} })^2 \\\\\n",
    "s^{corrected}_{dW^{[l]}} = \\frac{s_{dW^{[l]}}}{1 - (\\beta_1)^t} \\\\\n",
    "W^{[l]} = W^{[l]} - \\alpha \\frac{v^{corrected}_{dW^{[l]}}}{\\sqrt{s^{corrected}_{dW^{[l]}}} + \\varepsilon}\n",
    "\\end{cases}$$\n",
    "其中：\n",
    "- t 表示执行Adam的次数\n",
    "- L 神经网络的第几层\n",
    "- $\\beta_1$ 和 $\\beta_2$ 是用来控制指数加权平均值的两个超参数 \n",
    "- $\\alpha$ 是学习率\n",
    "- $\\varepsilon$ 用来避免除以0的情况\n",
    "\n",
    "和通常一样，我们将参数都存储在 `parameters` 字典中。 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**练习**: 初始化 Adam 变量 $v, s$ 用来记录之前的信息。\n",
    "\n",
    "**指导**: 变量 $v, s$ 初始化为一个值为零的python字典。 他们的keys和 `grads`相同:\n",
    "对于 $l = 1, ..., L$:\n",
    "\n",
    "```python\n",
    "v[\"dW\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"W\" + str(l+1)])\n",
    "v[\"db\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"b\" + str(l+1)])\n",
    "s[\"dW\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"W\" + str(l+1)])\n",
    "s[\"db\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"b\" + str(l+1)])\n",
    "\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: initialize_adam\n",
    "\n",
    "def initialize_adam(parameters) :\n",
    "    \"\"\"\n",
    "    Initializes v and s as two python dictionaries with:\n",
    "                - keys: \"dW1\", \"db1\", ..., \"dWL\", \"dbL\" \n",
    "                - values: numpy arrays of zeros of the same shape as the corresponding gradients/parameters.\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters.\n",
    "                    parameters[\"W\" + str(l)] = Wl\n",
    "                    parameters[\"b\" + str(l)] = bl\n",
    "    \n",
    "    Returns: \n",
    "    v -- python dictionary that will contain the exponentially weighted average of the gradient.\n",
    "                    v[\"dW\" + str(l)] = ...\n",
    "                    v[\"db\" + str(l)] = ...\n",
    "    s -- python dictionary that will contain the exponentially weighted average of the squared gradient.\n",
    "                    s[\"dW\" + str(l)] = ...\n",
    "                    s[\"db\" + str(l)] = ...\n",
    "\n",
    "    \"\"\"\n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "    v = {}\n",
    "    s = {}\n",
    "    \n",
    "    # Initialize v, s. Input: \"parameters\". Outputs: \"v, s\".\n",
    "    for l in range(L):\n",
    "    ### START CODE HERE ### (approx. 4 lines)\n",
    "        v[\"dW\" + str(l+1)] = np.zeros(parameters[\"W\" + str(l+1)].shape)\n",
    "        v[\"db\" + str(l+1)] = np.zeros(parameters[\"b\" + str(l+1)].shape)\n",
    "        s[\"dW\" + str(l+1)] = np.zeros(parameters[\"W\" + str(l+1)].shape)\n",
    "        s[\"db\" + str(l+1)] = np.zeros(parameters[\"b\" + str(l+1)].shape)\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    return v, s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v[\"dW1\"] = [[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "v[\"db1\"] = [[ 0.]\n",
      " [ 0.]]\n",
      "v[\"dW2\"] = [[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "v[\"db2\"] = [[ 0.]\n",
      " [ 0.]\n",
      " [ 0.]]\n",
      "s[\"dW1\"] = [[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "s[\"db1\"] = [[ 0.]\n",
      " [ 0.]]\n",
      "s[\"dW2\"] = [[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "s[\"db2\"] = [[ 0.]\n",
      " [ 0.]\n",
      " [ 0.]]\n"
     ]
    }
   ],
   "source": [
    "parameters = initialize_adam_test_case()\n",
    "\n",
    "v, s = initialize_adam(parameters)\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))\n",
    "print(\"s[\\\"dW1\\\"] = \" + str(s[\"dW1\"]))\n",
    "print(\"s[\\\"db1\\\"] = \" + str(s[\"db1\"]))\n",
    "print(\"s[\\\"dW2\\\"] = \" + str(s[\"dW2\"]))\n",
    "print(\"s[\\\"db2\\\"] = \" + str(s[\"db2\"]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**期望输出**:\n",
    "\n",
    "<table style=\"width:40%\"> \n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **s[\"dW1\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"db1\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"dW2\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"db2\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr>\n",
    "\n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**练习**:  用Adam实现参数更新。回顾参数更新公式： 对于 $l = 1, ..., L$: \n",
    "\n",
    "$$\\begin{cases}\n",
    "v_{W^{[l]}} = \\beta_1 v_{W^{[l]}} + (1 - \\beta_1) \\frac{\\partial J }{ \\partial W^{[l]} } \\\\\n",
    "v^{corrected}_{W^{[l]}} = \\frac{v_{W^{[l]}}}{1 - (\\beta_1)^t} \\\\\n",
    "s_{W^{[l]}} = \\beta_2 s_{W^{[l]}} + (1 - \\beta_2) (\\frac{\\partial J }{\\partial W^{[l]} })^2 \\\\\n",
    "s^{corrected}_{W^{[l]}} = \\frac{s_{W^{[l]}}}{1 - (\\beta_2)^t} \\\\\n",
    "W^{[l]} = W^{[l]} - \\alpha \\frac{v^{corrected}_{W^{[l]}}}{\\sqrt{s^{corrected}_{W^{[l]}}}+\\varepsilon}\n",
    "\\end{cases}$$\n",
    "\n",
    "**注意** 到第一次迭代 `l` 在 `for` 循环中应该为0， 而第一个参数是 $W^{[1]}$ and $b^{[1]}$。所以我们需要将`l` 表示为 `l+1` 。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters_with_adam\n",
    "\n",
    "def update_parameters_with_adam(parameters, grads, v, s, t, learning_rate = 0.01,\n",
    "                                beta1 = 0.9, beta2 = 0.999,  epsilon = 1e-8):\n",
    "    \"\"\"\n",
    "    Update parameters using Adam\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters:\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    grads -- python dictionary containing your gradients for each parameters:\n",
    "                    grads['dW' + str(l)] = dWl\n",
    "                    grads['db' + str(l)] = dbl\n",
    "    v -- Adam variable, moving average of the first gradient, python dictionary\n",
    "    s -- Adam variable, moving average of the squared gradient, python dictionary\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    beta1 -- Exponential decay hyperparameter for the first moment estimates \n",
    "    beta2 -- Exponential decay hyperparameter for the second moment estimates \n",
    "    epsilon -- hyperparameter preventing division by zero in Adam updates\n",
    "\n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    v -- Adam variable, moving average of the first gradient, python dictionary\n",
    "    s -- Adam variable, moving average of the squared gradient, python dictionary\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2                 # number of layers in the neural networks\n",
    "    v_corrected = {}                         # Initializing first moment estimate, python dictionary\n",
    "    s_corrected = {}                         # Initializing second moment estimate, python dictionary\n",
    "    \n",
    "    # Perform Adam update on all parameters\n",
    "    for l in range(L):\n",
    "        # Moving average of the gradients. Inputs: \"v, grads, beta1\". Output: \"v\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        v[\"dW\" + str(l+1)] = beta1 * v[\"dW\" + str(l+1)] + (1 - beta1) * grads[\"dW\" + str(l+1)]\n",
    "        v[\"db\" + str(l+1)] = beta1 * v[\"db\" + str(l+1)] + (1 - beta1) * grads[\"db\" + str(l+1)]\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Compute bias-corrected first moment estimate. Inputs: \"v, beta1, t\". Output: \"v_corrected\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        v_corrected[\"dW\" + str(l+1)] = v[\"dW\" + str(l+1)] / (1 - math.pow(beta1, t))\n",
    "        v_corrected[\"db\" + str(l+1)] = v[\"db\" + str(l+1)] / (1 - math.pow(beta1, t))\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Moving average of the squared gradients. Inputs: \"s, grads, beta2\". Output: \"s\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        s[\"dW\" + str(l+1)] = beta2 * s[\"dW\" + str(l+1)] + (1 - beta2) * grads[\"dW\" + str(l+1)] * grads[\"dW\" + str(l+1)]\n",
    "        s[\"db\" + str(l+1)] = beta2 * s[\"db\" + str(l+1)] + (1 - beta2) * grads[\"db\" + str(l+1)] * grads[\"db\" + str(l+1)]\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Compute bias-corrected second raw moment estimate. Inputs: \"s, beta2, t\". Output: \"s_corrected\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        s_corrected[\"dW\" + str(l+1)] = s[\"dW\" + str(l+1)] / (1 - math.pow(beta2, t))\n",
    "        s_corrected[\"db\" + str(l+1)] = s[\"db\" + str(l+1)] / (1 - math.pow(beta2, t))\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Update parameters. Inputs: \"parameters, learning_rate, v_corrected, s_corrected, epsilon\". Output: \"parameters\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        parameters[\"W\" + str(l+1)] = parameters[\"W\" + str(l+1)] - learning_rate * v_corrected[\"dW\" + str(l+1)] / np.sqrt(s_corrected[\"dW\" + str(l+1)] + epsilon)\n",
    "        parameters[\"b\" + str(l+1)] = parameters[\"b\" + str(l+1)] - learning_rate * v_corrected[\"db\" + str(l+1)] / np.sqrt(s_corrected[\"db\" + str(l+1)] + epsilon)\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "    return parameters, v, s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[ 1.63178673 -0.61919778 -0.53561312]\n",
      " [-1.08040999  0.85796626 -2.29409733]]\n",
      "b1 = [[ 1.75225313]\n",
      " [-0.75376553]]\n",
      "W2 = [[ 0.32648046 -0.25681174  1.46954931]\n",
      " [-2.05269934 -0.31497584 -0.37661299]\n",
      " [ 1.14121081 -1.09245036 -0.16498684]]\n",
      "b2 = [[-0.88529978]\n",
      " [ 0.03477238]\n",
      " [ 0.57537385]]\n",
      "v[\"dW1\"] = [[-0.11006192  0.11447237  0.09015907]\n",
      " [ 0.05024943  0.09008559 -0.06837279]]\n",
      "v[\"db1\"] = [[-0.01228902]\n",
      " [-0.09357694]]\n",
      "v[\"dW2\"] = [[-0.02678881  0.05303555 -0.06916608]\n",
      " [-0.03967535 -0.06871727 -0.08452056]\n",
      " [-0.06712461 -0.00126646 -0.11173103]]\n",
      "v[\"db2\"] = [[ 0.02344157]\n",
      " [ 0.16598022]\n",
      " [ 0.07420442]]\n",
      "s[\"dW1\"] = [[ 0.00121136  0.00131039  0.00081287]\n",
      " [ 0.0002525   0.00081154  0.00046748]]\n",
      "s[\"db1\"] = [[  1.51020075e-05]\n",
      " [  8.75664434e-04]]\n",
      "s[\"dW2\"] = [[  7.17640232e-05   2.81276921e-04   4.78394595e-04]\n",
      " [  1.57413361e-04   4.72206320e-04   7.14372576e-04]\n",
      " [  4.50571368e-04   1.60392066e-07   1.24838242e-03]]\n",
      "s[\"db2\"] = [[  5.49507194e-05]\n",
      " [  2.75494327e-03]\n",
      " [  5.50629536e-04]]\n"
     ]
    }
   ],
   "source": [
    "parameters, grads, v, s = update_parameters_with_adam_test_case()\n",
    "parameters, v, s  = update_parameters_with_adam(parameters, grads, v, s, t = 2)\n",
    "\n",
    "print(\"W1 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))\n",
    "print(\"s[\\\"dW1\\\"] = \" + str(s[\"dW1\"]))\n",
    "print(\"s[\\\"db1\\\"] = \" + str(s[\"db1\"]))\n",
    "print(\"s[\\\"dW2\\\"] = \" + str(s[\"dW2\"]))\n",
    "print(\"s[\\\"db2\\\"] = \" + str(s[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**期望输出**:\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "    <td > **W1** </td> \n",
    "           <td > [[ 1.63178673 -0.61919778 -0.53561312]\n",
    " [-1.08040999  0.85796626 -2.29409733]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b1** </td> \n",
    "           <td > [[ 1.75225313]\n",
    " [-0.75376553]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **W2** </td> \n",
    "           <td > [[ 0.32648046 -0.25681174  1.46954931]\n",
    " [-2.05269934 -0.31497584 -0.37661299]\n",
    " [ 1.14121081 -1.09245036 -0.16498684]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b2** </td> \n",
    "           <td > [[-0.88529978]\n",
    " [ 0.03477238]\n",
    " [ 0.57537385]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[-0.11006192  0.11447237  0.09015907]\n",
    " [ 0.05024943  0.09008559 -0.06837279]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[-0.01228902]\n",
    " [-0.09357694]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[-0.02678881  0.05303555 -0.06916608]\n",
    " [-0.03967535 -0.06871727 -0.08452056]\n",
    " [-0.06712461 -0.00126646 -0.11173103]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.02344157]\n",
    " [ 0.16598022]\n",
    " [ 0.07420442]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **s[\"dW1\"]** </td> \n",
    "           <td > [[ 0.00121136  0.00131039  0.00081287]\n",
    " [ 0.0002525   0.00081154  0.00046748]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"db1\"]** </td> \n",
    "           <td > [[  1.51020075e-05]\n",
    " [  8.75664434e-04]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"dW2\"]** </td> \n",
    "           <td > [[  7.17640232e-05   2.81276921e-04   4.78394595e-04]\n",
    " [  1.57413361e-04   4.72206320e-04   7.14372576e-04]\n",
    " [  4.50571368e-04   1.60392066e-07   1.24838242e-03]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"db2\"]** </td> \n",
    "           <td > [[  5.49507194e-05]\n",
    " [  2.75494327e-03]\n",
    " [  5.50629536e-04]] </td> \n",
    "    </tr>\n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "现在我们有三个优化算法(mini-batch gradient descent, Momentum, Adam)。让我们实现model()函数来分别运行他们并观察结果。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5 - Model - 使用不同优化算法\n",
    "\n",
    "我们使用\"moons\" 数据集来测试不同优化算法。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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pOWkUwU3qEtmtJb0/fpResx/xuC68Y1OfiT+B9aMuqz234tQsEn9ZR8qqHcgq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I8dQMdp/sebcSSfp+77GZdTx1HWW/bVJ1t48JmpxMSdCuKH9ufw9AO/4HR69TYL8ux8+OZ60lJy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\nv5qYYyZ0Z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      "text/plain": [
       "<matplotlib.figure.Figure at 0x105e08ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_X, train_Y = load_dataset()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们已经实现了一个3层神经网络，用它来测试三个优化算法算法： \n",
    "- Mini-batch **Gradient Descent**: 调用:\n",
    "    - `update_parameters_with_gd()`\n",
    "- Mini-batch **Momentum**: 调用:\n",
    "    - `initialize_velocity()` 和 `update_parameters_with_momentum()`\n",
    "- Mini-batch **Adam**: 调用:\n",
    "    - `initialize_adam()` and `update_parameters_with_adam()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def model(X, Y, layers_dims, optimizer, learning_rate = 0.0007, mini_batch_size = 64, beta = 0.9,\n",
    "          beta1 = 0.9, beta2 = 0.999,  epsilon = 1e-8, num_epochs = 10000, print_cost = True):\n",
    "    \"\"\"\n",
    "    3-layer neural network model which can be run in different optimizer modes.\n",
    "    \n",
    "    Arguments:\n",
    "    X -- input data, of shape (2, number of examples)\n",
    "    Y -- true \"label\" vector (1 for blue dot / 0 for red dot), of shape (1, number of examples)\n",
    "    layers_dims -- python list, containing the size of each layer\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    mini_batch_size -- the size of a mini batch\n",
    "    beta -- Momentum hyperparameter\n",
    "    beta1 -- Exponential decay hyperparameter for the past gradients estimates \n",
    "    beta2 -- Exponential decay hyperparameter for the past squared gradients estimates \n",
    "    epsilon -- hyperparameter preventing division by zero in Adam updates\n",
    "    num_epochs -- number of epochs\n",
    "    print_cost -- True to print the cost every 1000 epochs\n",
    "\n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    \"\"\"\n",
    "\n",
    "    L = len(layers_dims)             # number of layers in the neural networks\n",
    "    costs = []                       # to keep track of the cost\n",
    "    t = 0                            # initializing the counter required for Adam update\n",
    "    seed = 10                        # For grading purposes, so that your \"random\" minibatches are the same as ours\n",
    "    \n",
    "    # Initialize parameters\n",
    "    parameters = initialize_parameters(layers_dims)\n",
    "\n",
    "    # Initialize the optimizer\n",
    "    if optimizer == \"gd\":\n",
    "        pass # no initialization required for gradient descent\n",
    "    elif optimizer == \"momentum\":\n",
    "        v = initialize_velocity(parameters)\n",
    "    elif optimizer == \"adam\":\n",
    "        v, s = initialize_adam(parameters)\n",
    "    \n",
    "    # Optimization loop\n",
    "    for i in range(num_epochs):\n",
    "        \n",
    "        # Define the random minibatches. We increment the seed to reshuffle differently the dataset after each epoch\n",
    "        seed = seed + 1\n",
    "        minibatches = random_mini_batches(X, Y, mini_batch_size, seed)\n",
    "\n",
    "        for minibatch in minibatches:\n",
    "\n",
    "            # Select a minibatch\n",
    "            (minibatch_X, minibatch_Y) = minibatch\n",
    "\n",
    "            # Forward propagation\n",
    "            a3, caches = forward_propagation(minibatch_X, parameters)\n",
    "\n",
    "            # Compute cost\n",
    "            cost = compute_cost(a3, minibatch_Y)\n",
    "\n",
    "            # Backward propagation\n",
    "            grads = backward_propagation(minibatch_X, minibatch_Y, caches)\n",
    "\n",
    "            # Update parameters\n",
    "            if optimizer == \"gd\":\n",
    "                parameters = update_parameters_with_gd(parameters, grads, learning_rate)\n",
    "            elif optimizer == \"momentum\":\n",
    "                parameters, v = update_parameters_with_momentum(parameters, grads, v, beta, learning_rate)\n",
    "            elif optimizer == \"adam\":\n",
    "                t = t + 1 # Adam counter\n",
    "                parameters, v, s = update_parameters_with_adam(parameters, grads, v, s,\n",
    "                                                               t, learning_rate, beta1, beta2,  epsilon)\n",
    "        \n",
    "        # Print the cost every 1000 epoch\n",
    "        if print_cost and i % 1000 == 0:\n",
    "            print (\"Cost after epoch %i: %f\" %(i, cost))\n",
    "        if print_cost and i % 100 == 0:\n",
    "            costs.append(cost)\n",
    "                \n",
    "    # plot the cost\n",
    "    plt.plot(costs)\n",
    "    plt.ylabel('cost')\n",
    "    plt.xlabel('epochs (per 100)')\n",
    "    plt.title(\"Learning rate = \" + str(learning_rate))\n",
    "    plt.show()\n",
    "\n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "分别运行这三个不同的优化算法。\n",
    "\n",
    "### 5.1 - Mini-batch Gradient descent\n",
    "\n",
    "测试mini-batch gradient descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.690736\n",
      "Cost after epoch 1000: 0.685273\n",
      "Cost after epoch 2000: 0.647072\n",
      "Cost after epoch 3000: 0.619525\n",
      "Cost after epoch 4000: 0.576584\n",
      "Cost after epoch 5000: 0.607243\n",
      "Cost after epoch 6000: 0.529403\n",
      "Cost after epoch 7000: 0.460768\n",
      "Cost after epoch 8000: 0.465586\n",
      "Cost after epoch 9000: 0.464518\n"
     ]
    },
    {
     "data": {
      "image/png": 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wlqP9wbwuUpgT5yP9xTNK+yasgvvyLcOmajcjoVmSScVzpwwX6Qdu3ADAsQGj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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c4d8e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.796666666667\n"
     ]
    },
    {
     "data": {
      "image/png": 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QUloyb2BY3dRC5J6ncEoKy5abWuwg6h15vIgMZcShw3WUzlwNIZ4QOrsOVpLNKTWP+3re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zz0/W/4jZ7NT8RL9+zphpLyC8fvLD5y+Ge6c/cWo2t75Ryjy1uMrlWbttjsLHQaW6pEE5fs0hml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\nioiIhFCiFBERCfH/50bmP+Yj+ssAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a8a3668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train 3-layer model\n",
    "layers_dims = [train_X.shape[0], 5, 2, 1]\n",
    "parameters = model(train_X, train_Y, layers_dims, optimizer = \"gd\")\n",
    "\n",
    "# Predict\n",
    "predictions = predict(train_X, train_Y, parameters)\n",
    "\n",
    "# Plot decision boundary\n",
    "plt.title(\"Model with Gradient Descent optimization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,2.5])\n",
    "axes.set_ylim([-1,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 5.2 - Mini-batch gradient descent with momentum\n",
    "\n",
    "现在来看看加入momentum优化的效果。由于这个例子较简单，所以效果不是非常明显，再更复杂的例子中会有更好的表现。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.690741\n",
      "Cost after epoch 1000: 0.685341\n",
      "Cost after epoch 2000: 0.647145\n",
      "Cost after epoch 3000: 0.619594\n",
      "Cost after epoch 4000: 0.576665\n",
      "Cost after epoch 5000: 0.607324\n",
      "Cost after epoch 6000: 0.529476\n",
      "Cost after epoch 7000: 0.460936\n",
      "Cost after epoch 8000: 0.465780\n",
      "Cost after epoch 9000: 0.464740\n"
     ]
    },
    {
     "data": {
      "image/png": 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0SxQthiuQHesa+bPbtnLrtvbiJ1eATW0BBoJRDvQH86ZIAS5qN4ptSkmV9k0Y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\n+OEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c4c81d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.796666666667\n"
     ]
    },
    {
     "data": {
      "image/png": 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vH0vDbK0EVB2vC/msS6lYoj++v3Ntx3NzXOg/gZL6fabsNImQRb5hbJ5h2gpz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JaGxIR6QVqelopsntneLN1Tiyvf5MPXL+meXKBwYZbMUlDoe3ywi9n8GsnMjLGhnjAhrszHBqTD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\nYQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c755550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train 3-layer model\n",
    "layers_dims = [train_X.shape[0], 5, 2, 1]\n",
    "parameters = model(train_X, train_Y, layers_dims, beta = 0.9, optimizer = \"momentum\")\n",
    "\n",
    "# Predict\n",
    "predictions = predict(train_X, train_Y, parameters)\n",
    "\n",
    "# Plot decision boundary\n",
    "plt.title(\"Model with Momentum optimization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,2.5])\n",
    "axes.set_ylim([-1,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 5.3 - Mini-batch with Adam mode\n",
    "\n",
    "看看使用Adam会得到怎样的效果。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.690552\n",
      "Cost after epoch 1000: 0.185501\n",
      "Cost after epoch 2000: 0.150830\n",
      "Cost after epoch 3000: 0.074454\n",
      "Cost after epoch 4000: 0.125959\n",
      "Cost after epoch 5000: 0.104344\n",
      "Cost after epoch 6000: 0.100676\n",
      "Cost after epoch 7000: 0.031652\n",
      "Cost after epoch 8000: 0.111973\n",
      "Cost after epoch 9000: 0.197940\n"
     ]
    },
    {
     "data": {
      "image/png": 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rVGGyW0xo8TrykszSPRZEs8YNcO46L+IJgVe7J+b5q8LROeLHfzzTid8eGij0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\nVhouemZmVhr/By5RYeoKZjHhAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c7f7f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.94\n"
     ]
    },
    {
     "data": {
      "image/png": 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iebGz8CedMUIHTPcblUrA5ppLpaJIpYSxSfvYiqLCMAwtFFHYafXE66PMzjM/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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c75a518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train 3-layer model\n",
    "layers_dims = [train_X.shape[0], 5, 2, 1]\n",
    "parameters = model(train_X, train_Y, layers_dims, optimizer = \"adam\")\n",
    "\n",
    "# Predict\n",
    "predictions = predict(train_X, train_Y, parameters)\n",
    "\n",
    "# Plot decision boundary\n",
    "plt.title(\"Model with Adam optimization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,2.5])\n",
    "axes.set_ylim([-1,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 5.4 - 总结\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "        <td>\n",
    "        **optimization method**\n",
    "        </td>\n",
    "        <td>\n",
    "        **accuracy**\n",
    "        </td>\n",
    "        <td>\n",
    "        **cost shape**\n",
    "        </td>\n",
    "\n",
    "    </tr>\n",
    "        <td>\n",
    "        Gradient descent\n",
    "        </td>\n",
    "        <td>\n",
    "        79.7%\n",
    "        </td>\n",
    "        <td>\n",
    "        oscillations\n",
    "        </td>\n",
    "    <tr>\n",
    "        <td>\n",
    "        Momentum\n",
    "        </td>\n",
    "        <td>\n",
    "        79.7%\n",
    "        </td>\n",
    "        <td>\n",
    "        oscillations\n",
    "        </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>\n",
    "        Adam\n",
    "        </td>\n",
    "        <td>\n",
    "        94%\n",
    "        </td>\n",
    "        <td>\n",
    "        smoother\n",
    "        </td>\n",
    "    </tr>\n",
    "</table> \n",
    "\n",
    "Momentum 通常是有用的，但是由于学习率太小而且例子叫简单，所以对于结果的提升不明显。 \n",
    "\n",
    "Adam则表现的比mini-batch gradient descent 和 Momentum要好得多。如果你训练的够久，这三个模型都会得到不错的结果，但是我们已经看到Adam对模型带来的优化效果了。\n",
    "\n",
    "Adam的一些优点:\n",
    "\n",
    "- 相对小的内存需求 (虽然比 gradient descent 和 gradient descent with momentum要高) \n",
    "- 稍微调整就会有很好的效果 (除了 $\\alpha$)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**参考**:\n",
    "\n",
    "- Adam paper: https://arxiv.org/pdf/1412.6980.pdf"
   ]
  }
 ],
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